Theory of Games and Economic Behavior¶
von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
Cited by¶
16 citations across 16 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Axiom
- Ethical frameworks — deontological systems that name their supreme principle, and welfare-maximising systems that take a single criterion as axiomatic and derive policy from it. Economics — rationality, transitivity, and completeness of preferences as the axioms of choice theory, whose relaxation defines alternative behavioural models.
This sourceAxiomatizes rational choice — completeness, transitivity, and related axioms of preference — as the basis of expected-utility theory.
Supported in partVerified against the work's full text
Contents show an axiomatic treatment of preferences and utility, backing the economics clause only in frame; completeness and the behavioural-models clause are not evidenced.
“THE NOTION OF UTILITY 3.1. Preferences and utilities 3.2. Principles of measurement: Preliminaries 3.4. Principles of measurement: Detailed discussion 3.5. Conceptual structure of the axiomatic treatment of numerical utilities”
- Ethical frameworks — deontological systems that name their supreme principle, and welfare-maximising systems that take a single criterion as axiomatic and derive policy from it. Economics — rationality, transitivity, and completeness of preferences as the axioms of choice theory, whose relaxation defines alternative behavioural models.
- Competition
- The payoff to any agent is a function of the gap between its performance and that of its rivals, not of its absolute performance alone.
This sourceFounds the formal theory of games on the payoff structure — beginning with strictly competitive two-person zero-sum games (where payoffs sum to zero, so each agent's outcome turns on the gap with its rival) and generalizing to mixed-motive and cooperative games — defining competition as a relation among payoffs rather than an emotional register, with outcomes determined by relative rather than absolute performance.
- The payoff to any agent is a function of the gap between its performance and that of its rivals, not of its absolute performance alone.
- Duality
- … once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual and the LP dual
This sourceEstablished strong-duality/minimax connections for two-person zero-sum games. Precursor minimax theorem: von Neumann, "Zur Theorie der Gesellschaftsspiele." Mathematische Annalen 100 (1928): 295–320.
- … once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual and the LP dual
- Expected Utility
- The pattern was placed on a rigorous axiomatic footing by von Neumann and Morgenstern (1944), who showed that an agent whose preferences over risky prospects satisfy a short list of consistency conditions must behave as if maximizing the expectation of some utility function.
This sourceFirst rigorous axiomatization of expected utility: an agent whose preferences over risky prospects satisfy the consistency axioms behaves as if maximizing the expectation of a utility function
- The pattern was placed on a rigorous axiomatic footing by von Neumann and Morgenstern (1944), who showed that an agent whose preferences over risky prospects satisfy a short list of consistency conditions must behave as if maximizing the expectation of some utility function.
- Game-Theoretic Strategy
- The construct was introduced systematically by von Neumann and Morgenstern
This sourceFirst rigorous axiomatization of expected utility: an agent whose preferences over risky prospects satisfy the consistency axioms behaves as if maximizing the expectation of a utility function — the representation-theorem (not psychological-mechanism) reading, the separation of likelihood from value, and the formal core that makes the operation substrate-neutral.
- The construct was introduced systematically by von Neumann and Morgenstern
- Marginal Utility
- Marginal-utility reasoning extends naturally to uncertainty via expected utility theory (von Neumann and Morgenstern, 1944)
This sourceFirst rigorous axiomatization of expected utility: an agent whose preferences over risky prospects satisfy the consistency axioms behaves as if maximizing the expectation of a utility function — the representation-theorem (not psychological-mechanism) reading, the separation of likelihood from value, and the formal core that makes the operation substrate-neutral.
- Marginal-utility reasoning extends naturally to uncertainty via expected utility theory (von Neumann and Morgenstern, 1944)
- Minimax Strategy
- Minimax is mathematically rich: it sits at a fixed point of optimization duality, has clean saddle-point characterizations under convexity and concavity, and admits constructive solution methods — linear programming for finite zero-sum games, gradient descent-ascent for differentiable saddle problems, alpha-beta search for game trees.
This sourceSystematizes minimax solutions for zero-sum games, saddle points, and the duality underlying constructive solution methods.
Supported in partVerified against the work's full text
The book's table of contents shows chapters on zero-sum games, linearity and convexity, and the solution of all games by mixed strategies, supporting the minimax frame but none of the claim's duality, saddle-point, or algorithm clauses.
“LINEARITY AND CONVEXITY 16.1. Geometrical background 16.3. The theorem of the supporting hyperplanes 16.4. The theorem of the alternative for matrices 17. MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES”
- Minimax is mathematically rich: it sits at a fixed point of optimization duality, has clean saddle-point characterizations under convexity and concavity, and admits constructive solution methods — linear programming for finite zero-sum games, gradient descent-ascent for differentiable saddle problems, alpha-beta search for game trees.
- Mixed Strategy
- Two players simultaneously show a coin face; the matcher wins if the faces agree, the mismatcher if they differ — a zero-sum adversarial setting where each player's payoff depends entirely on predicting the other.
This sourceFounding text of game theory; develops the minimax solution and the role of randomization (mixed strategies) in games such as matching pennies where no pure equilibrium exists.
- Two players simultaneously show a coin face; the matcher wins if the faces agree, the mismatcher if they differ — a zero-sum adversarial setting where each player's payoff depends entirely on predicting the other.
- Non-Zero-Sum Game
- In economics, voluntary trade is paradigmatically non-zero-sum — both parties expect to gain or they would not trade — and gains-from-trade, comparative advantage, and welfare economics all rest on this, while financial speculation contains zero-sum components.
This sourceFounds game theory and the zero-sum versus non-zero-sum (non-constant-sum) distinction; establishes that joint payoff need not be conserved across strategy profiles.
- In economics, voluntary trade is paradigmatically non-zero-sum — both parties expect to gain or they would not trade — and gains-from-trade, comparative advantage, and welfare economics all rest on this, while financial speculation contains zero-sum components.
- Preference
- Preference is the foundational primitive on top of which the entire formal apparatus of consumer theory, choice theory, and welfare economics is built — from von Neumann and Morgenstern's (1944) expected-utility axiomatization to Samuelson's (1938) revealed-preference reconstruction of consumer demand without recourse to utility.
Supported in partVerified against the work's full text
The book's table of contents lists sections on preferences, utility, and the axiomatic treatment of numerical utilities, supporting the preference-based utility axiomatization but not the claim's sweeping historical framing.
“THE NOTION OF UTILITY 3.1. Preferences and utilities 3.2. Principles of measurement: Preliminaries 3.4. Principles of measurement: Detailed discussion 3.5. Conceptual structure of the axiomatic treatment of numerical utilities”
- Preference is the foundational primitive on top of which the entire formal apparatus of consumer theory, choice theory, and welfare economics is built — from von Neumann and Morgenstern's (1944) expected-utility axiomatization to Samuelson's (1938) revealed-preference reconstruction of consumer demand without recourse to utility.
- Risk
- Its defining structure has two parts that must co-occur: a probability assignment over outcomes (so the unknown is characterizable, not merely unknown) and a valuation that marks some outcomes as harmful.
This sourceFirst rigorous axiomatization of expected utility: an agent whose preferences over risky prospects satisfy the consistency axioms behaves as if maximizing the expectation of a utility function — the representation-theorem (not psychological-mechanism) reading, the separation of likelihood from value, and the formal core that makes the operation substrate-neutral.
- Its defining structure has two parts that must co-occur: a probability assignment over outcomes (so the unknown is characterizable, not merely unknown) and a valuation that marks some outcomes as harmful.
- Rock-Paper-Scissors (Intransitive Cyclic Dominance)
- In game theory, rock-paper-scissors itself has a unique Nash equilibrium at the uniform mixed strategy, because no pure choice dominates.
This sourceEstablishes the minimax theorem and the unique mixed-strategy equilibrium of symmetric zero-sum games such as rock-paper-scissors at (1/3, 1/3, 1/3).
- In game theory, rock-paper-scissors itself has a unique Nash equilibrium at the uniform mixed strategy, because no pure choice dominates.
- Zero Sum Game
- It enables reasoning about the minimax structure: in finite two-player zero-sum games optimal strategies exist and yield a single value of the game, the simplest equilibrium concept, and the foundation for adversarial optimisation in machine learning.
This sourceFoundational treatment of zero-sum games and the minimax solution as the simplest equilibrium concept.
Supported in partVerified against the work's full text
The fetched Princeton page is the book's table of contents and jacket copy: it shows the volume covers zero-sum restrictions and strictly determined games, but states neither the minimax value result nor any machine-learning use.
“The meaning of the zero-sum restriction”
- It enables reasoning about the minimax structure: in finite two-player zero-sum games optimal strategies exist and yield a single value of the game, the simplest equilibrium concept, and the foundation for adversarial optimisation in machine learning.
Domain-specific¶
Mechanisms¶
- Dominance Violation Scan
- Its strength is that it is a cheap, unambiguous filter: a genuine dominance violation is a logical impossibility for a coherent chooser, so a flag is high-signal and demands explanation — usually a data problem, a hidden option, or a choice-environment defect — before any modeling proceeds.
This sourceFormalizes coherent preference comparisons under which a rational chooser cannot prefer an alternative that is dominated in every relevant payoff comparison.
- Its strength is that it is a cheap, unambiguous filter: a genuine dominance violation is a logical impossibility for a coherent chooser, so a flag is high-signal and demands explanation — usually a data problem, a hidden option, or a choice-environment defect — before any modeling proceeds.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 4 of 16 citations: 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://search.worldcat.org/title/1629708 ×1
- https://www.degruyterbrill.com/document/doi/10.1515/9781400829460/html ×1
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